Unformatted text preview: First Order Logic (Predicate Calculus) CPS 170 Ronald Parr Limita<ons of Proposi<onal Logic • Suppose you want to say: All humans are mortal • For ~6B people, you would need ~6B proposi<ons • Suppose you want to stay that (at least) one person has perfect pitch • You would need a disjunc<on of ~6B proposi<ons • There has to be a beMer way… 1 First Order Logic • Proposi<onal logic is very restric<ve – Can’t make global statements about objects in the world – Workarounds tends to have very large KBs • First order logic is more expressive – Rela<ons, quan<ﬁca<on, func<ons – but… inference is trickier First Order Syntax • Sentences • Atomic sentence predicate(term) • Terms – func<ons, constants, variables • Connec<ves • Quan<ﬁers • Constants • Variables 2 Rela<ons • Assert rela<onships between objects • Examples – Loves(Harry, Sally) – Between(Canada, US, Mexico) • Seman<cs – Object and predicate names are mnemonic only – Interpreta<on is imposed from outside – O_en we imply the “expected” interpreta<on of predicates and objects with suggested names Func<ons • Func<ons are specials cases of rela<ons • Suppose R(x1,x2,…,xn,y) is such that for every value of x1,x2,…,xn there is a unique y • Then R(x1,x2,…,xn) can be used as a shorthand for y – Crossed(Right_leg_of(Ron), Le__leg_of(Ron)) • Remember that the object iden<ﬁed by a func<on depends upon the interpreta<on 3 Quan<ﬁca<on • For all objects in the world… ∀xhappy( x )
• For at least one object in the world… € ∃xhappy( x )
€ Examples • Eve...
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This note was uploaded on 02/17/2012 for the course COMPSCI 170 taught by Professor Parr during the Spring '11 term at Duke.
 Spring '11
 Parr
 Artificial Intelligence

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